Accelerated Dimension-Independent Adaptive Metropolis

Yuxin Chen, David E. Keyes, Kody J H Law, Hatem Ltaief

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


This work describes improvements by algorithmic and architectural means to black-box Bayesian inference over high-dimensional parameter spaces. The well-known adaptive Metropolis (AM) algorithm [H. Haario, E. Saksman, and J. Tamminen, Bernoulli, (2001), pp. 223--242] is extended herein to scale asymptotically uniformly with respect to the underlying parameter dimension for Gaussian targets, by respecting the variance of the target. The resulting algorithm, referred to as the dimension-independent adaptive Metropolis (DIAM) algorithm, also shows improved performance with respect to adaptive Metropolis on non-Gaussian targets. This algorithm is further improved, and the possibility of probing high-dimensional (with dimension $d \geq 1000$) targets is enabled, via GPU-accelerated numerical libraries and periodically synchronized concurrent chains (justified a posteriori). Asymptotically in dimension, this GPU implementation exhibits a factor of four improvement versus a competitive CPU-based Intel MKL (math kernel library) parallel version alone. Strong scaling to concurrent chains is exhibited, through a combination of longer time per sample batch (weak scaling) with fewer necessary samples to convergence. The algorithm performance is illustrated on several Gaussian and non-Gaussian target examples, in which the dimension may be in excess of one thousand.
Original languageEnglish (US)
Pages (from-to)S539-S565
Number of pages1
JournalSIAM Journal on Scientific Computing
Issue number5
StatePublished - Oct 27 2016

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work was supported by the King Abdullah University of Science and Technology
(KAUST). The work of the third author was partially supported by Oak Ridge National Laboratory
Directed Research and Development Strategic Hire grant 32112590 LDRD


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